Space of modular forms of level 980, weight 1, and Character 980.f

• Label: 980.1.f
• Level: $980$
• Weight: $1$
• Character orbit: 980.f
• Rep. character: $\chi_{980}(99,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $5$
• Sturm bound: $168$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	980.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(168\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(980, [\chi])\).

	Total	New	Old
Modular forms	24	18	6
Cusp forms	8	8	0
Eisenstein series	16	10	6

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

\( 8 q - 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(980, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
980.1.f.a	$980$	$1$	980.f	20.d	$2$	$1$	$1$	$0.489$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-5}) \)	None	✓	$2$	$0$	\(-1\)	\(-1\)	\(-1\)	\(0\)	$1$		\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
980.1.f.b	$980$	$1$	980.f	20.d	$2$	$1$	$1$	$0.489$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-5}) \)	None	✓	$2$	$0$	\(-1\)	\(1\)	\(1\)	\(0\)	$1$		\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
980.1.f.c	$980$	$1$	980.f	20.d	$2$	$1$	$1$	$0.489$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-5}) \)	None	✓	$2$	$0$	\(1\)	\(-1\)	\(1\)	\(0\)	$1$		\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
980.1.f.d	$980$	$1$	980.f	20.d	$2$	$1$	$1$	$0.489$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-5}) \)	None	✓	$2$	$0$	\(1\)	\(1\)	\(-1\)	\(0\)	$1$		\(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
980.1.f.e	$980$	$1$	980.f	20.d	$2$	$4$	$4$	$0.489$	\(\Q(\zeta_{8})\)	$D_{4}$	\(\Q(\sqrt{-1}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{8}^{2}q^{2}-q^{4}-\zeta_{8}q^{5}-\zeta_{8}^{2}q^{8}+\cdots\)